Calculate Plane Speed from Diameter & Angle

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To calculate the speed of a plane traveling in a circular path with a diameter of 32 km and banking at an angle of 12 degrees, the sideward acceleration of 2.1 m/s² is crucial. The relationship between the banking angle and sideward acceleration can be expressed using the equation v² = a * radius * tan(angle). By applying this formula, a calculated speed of 84.5 m/s was derived. The diameter and angle are essential for determining the radius and the resultant forces acting on the plane. This method effectively combines geometry and physics to find the required speed.
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A plane is traveling in a circular path 32 km in diameter. It is banking at an angle of 12o, which indicates that its sideward acceleration is 2.1m/s2. What is its speed?


So I can use v=at, but I don't know time. What am I suppose to do with the 32km and the angle of 12?
 
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ok so how does the banking angle indicate the sideward acceleration?
 
is it possible to use the equation v^2 = a * radius * tan angle?
 
From using that equation I got speed to be 84.5m/s...does that sound right?
 
Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
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